In this paper we obtain the criterion of weak convergence of the sequence of the sum of the first $n$ terms of the linear process $\left\{X_{kn} ,\; k=1,2,...,n;\; n=1,2,...\right\}$ with random coefficients $\left\{v^{k} ,k\in {\mathbb N}\right\}$, generated by the innovation sequence $\left\{\xi _{kn} ,k\in Z\right\}$ satisfying the condition of infinite smallness to the limit distribution and as a consequence of this result we obtain the analog of the Lindeberg-Feller theorem for the auto regression process with random parameter $v,\; 0{\rm \; }<{\rm \; }v<1$. In addition, the strong law of large numbers and the law of iterated logarithm are proved.
| Mualliflar | T.M.Zuparov, A.I.Jovliev |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 176-180 |
| DOI | 10.29229/uzmj.2025-3-19 |
DOI: 10.29229/uzmj.2025-3-19 · Maqolaning asl sahifasi
Auto regression process, linear process, central limit theorem, strong law of large numbers, law of iterated logarithm
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